I am planning a 1 day trip to Mount Koya during a short stay in Osaka. Please let me know if you have done this and how you went about it and any other helpful feedback you may have. Thank you.

For information about how to do it:
https://www.japan-guide.com/e/e4904.html

There are some very interesting temples on Koyasan, but I trust you realize that one of the delights of visiting there is to spend a night in a temple.

We did it a few years ago. Coincidentally I was just looking at transferring the details over from our old to our new blog. We travelled from Kyoto rather than Osaka but it was a bit of a convoluted journey involving:
a bus to Kyoto station,

• The Super-Express to Wakayama
• a local train to Hashimoto
• another local train to Gorigushi
• the funicular railway to Koyasan station
• a bus into town.

a day trip would be long and involved and I would strongly suggest staying overnight at one of te temples. We stayed at Eko In and loved it. The deal involved dinner and breakfast (and the food was amazing), a morning service at the temple. We spent two nights there and used it to explore the temples around th town with the aid of a volunteer guide and paid day and night visits to Okonuin. A highlight of our time in Japan.

I cant find my notes, but I think we booked the temple either with https://www.japaneseguesthouses.com/

Please note that there is some issue with the train track to Koyasan due to the typhoon in October, so you have to take a substitute bus which can take longer (see also japan guide-mount koya acces and orientation)

We still went there and it was worthwhile, but thoroughly recommend to stay the night (that was the highlight).

I recommend staying the night. As that is the best part and a day trip would be a long day. However, it’s less involved than it looks; the local trains/buses are coordinated time wise, and it’s an easy, though time consuming trip.

You could see the sights with an early morning start, but as others have suggested, it's far better to experience Koyasan - and walking around after all the day trippers left gives a wholly different atmosphere.
For transport, consider the Koyasan World Heritage Ticket. For places to stay, try Shukubo.net